SOLVED!
When I last posted I was about to disconnect the exhaust to see if it was blocked. After having a relative put his hands over the tailpipes we found that pressure was developing in both of them during the 4 seconds the engine was running and therefore assumed the exhaust/cat was not blocked.
Someone suggested it might be the key transponder antenna ring around the ignition keyhole. I think I eliminated this by sitting in the car, using the remote to lock the car and activate the alarm, then putting the key in the ignition and watching the alarm light stop flashing when I turned the key to the on position. My logic was that the car "recognized" the key, but that may be wishful thinking.
My relative decided to try something new: he disconnected the electrical connection to the MAF. The engine started and ran, not well, but it ran!
I had cleaned the MAF earlier but not checked it in any other way and it was not throwing any code.
A new MAF sensor solved the problem.
Lessons learned:
- A bad MAF will shut down the engine within seconds after start up.
- The engine will run with the MAF disconnected electrically, so this may be a good way to check for a bad MAF.
- A bad MAF does not always throw a code.
My troubleshooting was not cheap but I now have spare Crank and Camshaft position sensors and a Relay Control Module, and I'm pretty sure it cost no more than taking it to the dealer..
Thank you everyone who made suggestions.